Unit handling (was: Another Idea for Ada 20XX)

[Wilhelm Spickermann <wilhelm.spickermann@t-online.de>]

--On Monday, December 03, 2001 13:34:09 +0100 Dirk Dickmanns 
<Dirk.Dickmanns@BMW.de> wrote:

...
> Besides the work of Lutz, I have:
> http://users.erols.com/whitaker/iss_418.htm
> http://www.dmitry-kazakov.de/ada/units.htm
>

May I add some of my ideas here? They could be realized as an 
optional ASIS program checker or as a compiler component and 
would not have any execution time penalty or require the tools 
to be available to do the compilation. As unit consistency is a 
program property, it´s not really necessary to have the tool on 
every platform and every site.

The idea is to define the basic SI-Units as named numbers with 
value 1.0 and using values like "5.7 * meter / second" in the 
program. (The compiler can easily optimize such expressions.)

A pragma for use by ASIS (or the compiler) defines which Units 
are to be viewed as basic.

Every variable, constant, parameter or named number will be 
associated with a derived unit upon the first assignment seen, 
by tracking the operations down to the basic units and all 
following assignments will be required to lead to the same 
result. Additionally all operations will be checked for 
consistency. (As others have already pointed out, there are not 
too many operations to be considered, as operations like taking 
the logarithm of something can never be applied to something 
having a unit)

An additional ASIS-pragma can assign a derived unit to a 
variable or parameter where the unit is not associated 
implicitly by an initial or default value.

A first sketch using SI as an example:

package Units is
   --  The 7 SI units:
   Meter : constant := 1.0;
   ...
   pragma Define_Unit (Meter, Kilogram, Second, Ampere,
                       Kelvin, Candela, Mole);
   ...
   --  SI derived units:
   Newton : constant := Meter * Kilogram / Second**2;
   ...
   --  SI accepted derived units:
   Liter : constant := 1.0e-3 * Meter**3;
   ...
end Units;

(No special handling for the child units needed, they just 
collect some definitions and try to convince programmers, that 
that it´s a bad idea to define a factor "Billion" etc.)

package Units.More is
   --  Defined (not experimentally determined) units.
   Foot : constant := 0.3048 * Meter;
   Foot_US_Survey : constant := Foot / 0.999998;
   ...
   --  experimentally determined units / constants
   Electron_Volt : constant := 1.602_177_33e-19 * Joule;
   ...
end Units.More;

package Units.Factors is
   ...
   Kilo  : constant := 1.0E3;
   ...
   Billion_US_FR : constant := 1.0E9;
   Billion_OTH : constant  := 1.0E12;
   ...
   Kilo_Binary : constant := 2.0**10;
   ...
end Units.Factors;

I think this notation is readable and could be helpful even 
without any tool to do the checks. It does not create any 
runtime penalties. It should be possible to implement the 
checker in ASIS or as an additional compiler component which may 
be switched on or off. It´s not meant as a proposal for Ada 
20XX, but if someone  would like to view it as one: it would 
only introduce conflicts in the two new pragma names.

(It will however not be able to handle units like "decibels" or 
"degrees celsius". I view these as pseudo units which only make 
mathematical reasoning impossible. They should occur only in the 
user interface as common expressions, but I´ve written that in 
another mail.)

Wilhelm